A Thing of Beauty is Joy for Ever

Re: # 11 then folio you should listen/read to the stuff some of the people here write - they are very very god maths wizards (and I kid you not) - irrespective of what some guys here say

Dash, Coz mathematics is the most colourless, heartless subject from the teachers' pov. We use to get into 'maths mode' to get 'marks' than 'learn' it as a tool to unravel the world around us.

Yes I meant compliment (based on previous posts on Maths).

Re: # 9 :D :D strange you ask that.....I do not have the mind for that kind of thing, it way to cluttered for clear thinking. Though I take your comment as a compliment. :D

Dash, It's strange that a guy like u spending time on Chowk i/o teaching innovators @ Industrial Design Engg, IIT or eccentrics @ NID, Ahd.

Re: # 7 BTW this is different from my question belwo to Gill (the beauty thing)

Re: # 5

Beauty is in the compactness of a solution - to represent a complex formulation. Thus Penrose's argument is correct in that most AI stuff are way to complex both from an analytical point of view and from a computation point of view.

Similarly Djikstra's critique: how many time have we marvelled at the ability of a programmer to compress code to a few kb, when ordinary mortals use a few mb for the same. What he did was to eliminate lazy programming, and make sure the programmer thought before coding. IMHO His notion of cleanness is more to introduce the ability to read and control flow of instructions, where as compactness was not necessarily the primary motive.

I tried posting yesterday - but didnot realise I was incarcerated....

but I have a question for GIll (and perhaps a comment).

What exactly do you mean by beauty of Mathematics (the two equations you give and the the examples you use)?


Every mathematical model has to do two/three things

(a) it has to be an accurate representation of the present
(b) to be an accurate representation of the present, it has to be an accurate representation of the past
(c) given (b) and (a) it has to be a good representation of the future

(b) is essentially an interpolation exercise (a) is a one-step-ahead prediction exercise whilst (c) is an n-step ahead exercise (extrapolation). Without these the model is useless? Where is the beauty in this?

Very interesting Mr. Gill.

The underlying hypothesis of your article is that Truth must be beautiful.

i.e. one test of a mathematical or scientific theory is "Is it beautiful?".

It is an axiom for many scientists.

Roger Penrose for example used this axiom to critique current theories of Artificial Intelligence saying they were not beautiful enough to be true (See Emperor's New Mind)

Similarly the computer scientist Edsger Djikstra used this to critique the clutter in programming languages saying "Beauty is our business". This critique influenced the creation of 'cleaner' programming language models such as block structuredness and removal of arbitrary control flow constructs such as gotos.

At the same time, it is often observed by engineers that reality is messy and solutions that are aimed not at abstracted realities but at the real world in a sense have to share in this messiness. Somewhere along the way mathematical elegance gives way to pragmatism and utilitarianism. This could be the reason why in software development, formally beautiful language models such as functional programming or logic programming have lost out to 'ugly' models such as object oriented models and the never ending world of scripts. They are messy but they work.

One could also say that engineers also have their own standard for beauty.

Except the maths geek Iron nobody bothered to write here.:(

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the reason is simple:

Mathematical laws/results are the ultimate truth

everything else is up for an argument, but a mathematical solution does not require an argument to prove that it is right